I'm a big fan of scavenger hunts as a way to introduce and reinforce a concept! I don't remember where I got this one from (if it was from you, let me know so can give you credit) but I'm going to use it when I introduce synthetic division in pre-cal on Monday.
Synthetic Division Scavenger Hunt
Friday, February 22, 2013
My Weekly Diigo Bookmarks (2/22/13)
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Interactive Mathematics - Learn math while you play with it!
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The Components of Number Sense: An Instructional Model for Teachers
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Free Social Teaching and Learning Network focused solely on education
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How to evaluate students’ effort on out-of-class work in a flipped class
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Observations First: Practicing Struggle at Home and in Class
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Studies of the Effects of Formative Assessment on Student Achievement: So Much More is Needed
Friday, February 15, 2013
Function Composition Relay
I've taught function composition in Algebra II and in Pre-Calculus, and my students ALWAYS seem to struggle with it. I remember it actually bringing a girl to tears in one of my first years of teaching. So this year I decided to try and try a more informal approach to introduce the concept in hopes that it would make something "click" for my students.
I printed this out and cut apart the functions.
Function Composition Relay
Each person in a group got a different function. Then I wrote on the board the definitions of composition (f (g(x)) and g(f(x))) and explained that it was like a relay, with the inside handing off to the outside. I started with an example of composition on a number: f(g(2)) and explained that this meant that g would take the 2 and do "its thing" to the 2, then hand off the result to f and then f would do "its thing" and get the final result. I posted several more examples of composition on a number on the board, one at a time, and had them calculate the results in their group. We even did composition of three and even four functions. Then I asked them "What if I want to know a formula for the relay so that I don't have to actually do the relay in order to figure out how it turns out? In other words, what if I want to find the composition on x?" We then did f(g(x)) together. They were able to do any combination of function composition I put on the board, including (with a little help) the f(g(h(j(x)) composition. It went great! I will definitely be teaching composition as a relay from now on.
I will say that my students still struggled to recognize the symbol for composition when it showed up on the test. If I reminded them that it was the "relay" operation, they would go "oh, yeah!", so I'm going to have to give them some more independent practice with the notation next year....
I printed this out and cut apart the functions.
Function Composition Relay
Each person in a group got a different function. Then I wrote on the board the definitions of composition (f (g(x)) and g(f(x))) and explained that it was like a relay, with the inside handing off to the outside. I started with an example of composition on a number: f(g(2)) and explained that this meant that g would take the 2 and do "its thing" to the 2, then hand off the result to f and then f would do "its thing" and get the final result. I posted several more examples of composition on a number on the board, one at a time, and had them calculate the results in their group. We even did composition of three and even four functions. Then I asked them "What if I want to know a formula for the relay so that I don't have to actually do the relay in order to figure out how it turns out? In other words, what if I want to find the composition on x?" We then did f(g(x)) together. They were able to do any combination of function composition I put on the board, including (with a little help) the f(g(h(j(x)) composition. It went great! I will definitely be teaching composition as a relay from now on.
I will say that my students still struggled to recognize the symbol for composition when it showed up on the test. If I reminded them that it was the "relay" operation, they would go "oh, yeah!", so I'm going to have to give them some more independent practice with the notation next year....
Math = Love (The Outcome)
I posted earlier this week that my students would be making math-themed valentine's while I was out with a sick kid. It was such a fun surprise to return to work and find these waiting for me. The kids did a fabulous job, so I thought I'd post a few of my faves.
And here's one from a student who used every word on the list IN ORDER. Very impressive!
Tuesday, February 12, 2013
Multiplicity
Last week we started our study of Polynomial Functions in Pre-Cal with a discussion of end behavior, followed up with this worksheet to check for understanding. So now that we know what the ends of the graph are doing, we move to what happens in the middle, or what I call "the wiggle". I think I'm going to use a combination of these two activities, but I'm not sure yet what order I'll do them in. I'm thinking I'll use the first one to introduce the concept of zeros and multiplicity and then do the second one to reinforce. I've taken a completely different approach to this topic this year - I haven't ever been happy with the way the book teaches polynomials - and I'm hoping that this approach will help my students see the "big picture" instead of just teaching them a bunch of seemingly unrelated topics and processes.
Math = Love
I've been out with a sick kiddo this week, and I hate just leaving boring old worksheets for my students to do with the sub, so I was excited when I saw this in my Twitter feed yesterday! I retyped it to give some specific instructions to my students and to add a few Calculus specific vocabulary words to the list. I talked with my sub (a former teacher and assistant principal who retired but still comes back to sub) and he felt comfortable letting the kids get a little creative today. I can't wait to see what they come up with! It'll be so much more fun to "grade" these when I get back than it would have been to have a worksheet waiting for me.
Math Valentines
Math Valentines
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